Existence of solutions for perturbed fractional equations with two competing weighted nonlinear terms. (English) Zbl 1499.35687
Summary: This paper deals with a perturbed nonlocal equation of fractional Laplacian type involving two competing nonlinear terms with weights \(f\) and \(h\). Under two kinds of integrability conditions on the ratio of \(f\) to \(h\), we show some different existence results in this setting by using variational methods. Our results are extension of some problems studied by G. Carboni and D. Mugnai [J. Differ. Equations 262, No. 3, 2393–2413 (2017; Zbl 1352.35217)] and M. Xiang et al. [J. Differ. Equations 260, No. 2, 1392–1413 (2016; Zbl 1332.35387)].
MSC:
| 35R11 | Fractional partial differential equations |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35J20 | Variational methods for second-order elliptic equations |
| 35J60 | Nonlinear elliptic equations |
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